# Can a spin-flip TD-DFT singlet ground state wavefunction be written as a sum over MOs with occupancy information?

Using collinear spin-flip(SF) TD-DFT with the Tamm-Dancoff approximation, BHanHLYP and a simple test molecule (ethene, with a singlet ground state).

It's my understanding, using ethene as an example, that spin-flip DFT starts with a unrestricted Kohn-Sham single-reference triplet reference state, then generates the other TD-DFT 'excited' states using the MOs and occupancies from that reference state and a calculated excitation vector. The relative energy of the ground state can be calculated, and, at least in ORCA, the molecular geometry can be optimized on this ground-state PES. So far, so good.

My question is: can the wavefunction of the resulting singlet SF ground state, which appears as an effective negative-energy 'excited' state, have its electron density distribution represented (and written in machine-readable form), as another set of only MOs and occupancies?

It doesn't matter if this output set is single-reference or multi-reference, for my purposes, just so long as it can be output as only MOs and occupations.

If this is implementation-dependent, which codes implementing spin-flip TD-DFT can do this? Does the Tamm-Dancoff approximation need to be dropped in order to achieve this?

$$D = \sum_i n_i |\psi_i\rangle \langle\psi_i| \tag{1}$$